Andy Murray lost the opening set but appeared the have an advantage in the second. Photograph: Pierre-Philippe Marcou/AFP

If there are still critics of Andy Murray south of the border, their numbers, surely, must be dwindling. The finest player Britain has produced since Fred Perry burnished his soaring reputation here in the semi-final of the ATP Masters Madrid by beating Roger Federer 3-6 6-3 7-5.

Murray will now play the rising French star Gilles Simon, who battled Rafael Nadal in an extraordinary 3hr 22min marathon and came through to win 3-6 7-5 7-6, winning the tiebreak 8-6. Simon, who had saved six match points in earlier matches, says he never gets tired. Murray will test that today.

It was Murray's third victory over the former world No1 in five meetings and offered some measure of revenge for the defeat he suffered against Federer in last month's US Open final. Despite being unable to prevent Britain losing to Austria in the Davis Cup, there is very little Murray has done wrong in the past three months and, if anything, his world ranking of No 4 looks beneath him. With Novak Djokovic going off the boil, the 21-year-old Scot has certainly looked like the third best player in the world since August, especially as he beat Djokovic in successive weeks at Toronto and Cincinnati.

His reputation in the place where it counts most, the tour locker room, is that of a player who has it all. Any coach and most rivals will talk to you about his unerring accuracy off the ground, his fine serve and his deceptive speed. And Federer, in particular, talks of his tactical acumen - the ability to think on his feet and change his approach if things are not going his way.

That is precisely what he needed to do here yesterday after a tentative first set that had seen him still unable to shake off the nerves he had felt when facing his legendary opponent in his first Grand Slam final in New York. The previous day he had spoken of being more relaxed here - which was only natural, given the fact that he had not had to face Nadal in a protracted battle over two days, as he did at the US Open - as well as the brilliance of his own form while dismissing as good a player as Gaël Monfils 6-2 6-2 here in the quarter-finals.

But there was no doubt Federer deserved the first set, partially as a result of the kind of errors that cost Murray the break in the sixth game - a forehand that sailed long. But there were no histrionics, an improvement in his game that Federer noted afterwards.

'You need to give young guys time to learn,' said Federer, who had temperament problems of his own in his teens. 'It's fun to see them learning.' But the Swiss found it less fun to see how Murray was able to turn the match around; slowly pressing the accelerator until his game took on a more aggressive mode.

At deuce in the fourth game of the second set, Murray unleashed a superb forehand service return that Federer hardly saw and was in at the net on the break point to finish the game. Murray never allowed Federer a sniff of a break back as he levelled the match and, despite having to stave off a break point at 0-1 in the third, he seemed to have taken control when he got Federer 0-40 down in the third game. But Federer was playing at close to his best and reeled off five consecutive points to hold.

Murray, looking composed by this stage, had another break point at 2-2, but Federer's responses were helping to elevate the contest to the kind of duel the capacity 9,600 crowd wanted.

Murray continued to serve with great authority - he had not lost a point on his first serve in the second set - and with his returns starting to bite, Federer found himself facing another break point in the 11th game. After a great rally, the sting in the Scottish backhand was enough to force the error. Two aces helped Murray served out for this memorable victory

'I am playing great tennis; yesterday I played great but with all respect to Gaël Monfils [whom he beat in the quarter-final], he is not Federer,' said Murray. 'First, with Federer and Nadal, the respect you have for them is greater and when they are behind they are always going to come back at you. So it's tough to dictate a match. But I served huge; my second serve was very good. I stayed calm and found the big shot at the right time.'